Neither side in the EU referendum debate is covering itself with glory. Rational voters can only despair when they see public money spent on propaganda, or sensationally daft numbers based on bizarre assumptions – or prophesies that Brexit would plunge us into war.

They must also despair at the Leave side, one of whose main ads implores them to ‘Save the NHS on June 23’. Pardon? Yes, it continues, Brussels wastes £350 million of our cash – “enough to build one new hospital” – every week. But things will get even worse. The euro is broken, so we will be roped in for bailouts. And the EU plans to admit five new countries: so “what will happen to our public services?”

For my part, I think we should leave the EU. I did not always think so: as a student, I campaigned to remain in the ‘common market’. For a free-market liberal like me, it seemed win-win. As the ‘market’ became a ‘community’ and then a ‘union’, I still believed that the economic gains offset the creeping centralisation. That changed when Tony Blair signed us up to the Social Chapter and a slew of employment regulation. Then, I figured, both sides of the equation had become negative.

At least my decision was a rational one. But both sides in this campaign pander to our least rational, most visceral emotions. It is hard to get away from Project Fear, or for that matter, Project Get Endorsement From Some International Establishment Elite That Hasn’t The Foggiest What It Actually Means To Sink Your Sovereignty Into An Undemocratic Centralising Bureaucracy.

But telling us to vote Brexit to save the NHS really is the pits. For a start, there is a nasty niff of nationalism in the (carefully understated) threat that hordes of Turks, Serbians, Albanians, Montenegrans and Macedonians will swamp our public services.

Never mind the fact that there is slim chance of Greece (or even the UK) letting in Turkey, whose population outnumbers all the others by six to one. The real problem is not the potential immigration, but the fact that our public services can’t cope with it because they are state-run and taxpayer funded. You never hear Tesco complaining about having too many customers.

I favour free movement on economic and libertarian grounds, though if anyone is to control our borders, it should be us and not Brussels. As for the £350 million a week that we would supposedly liberate in order to shore up the NHS, my advice is not to believe any number produced in this campaign: they are all flaky. We certainly would make some saving from Brexit: half or two-thirds of that, no sweat; maybe more when Margaret Thatcher’s rebate runs out shortly. But would that enable us to build a new hospital every week? Hardly.

For a start, even the fanciful £350 million a week is a drop in an NHS budget of well over £100 billion a year. Even if the £350 million figure were correct, there would of course be plenty of other things to spend it on. For a start, our agriculture and car making industries are highly dependent on the subsidies and protectionism afforded by the EU. These are bad policies, but we might want to use some a Brexit windfall in trying to wean these sectors off the teat, rather than just letting them collapse. And there would be other transition costs.

We might use the money to restructure the welfare system, and produce the simple, fair, high-incentive system that Iain Duncan Smith wanted, and which George Osborne starved of transition funds.

Or, if you wanted a really radical suggestion – deeply unfashionable these days, I know – we could actually give the Brexit windfall back to the public and lower their taxes. That would raise incentives and boost economic growth.

So if the question is whether we want to “keep sending hundreds of millions to the EU every week, or vote to put that money into our priorities such as the NHS and the Cancer Drugs Fund,” it is a pretty silly one.

This appeal to “save the NHS” is already backfiring. On a visit to the US, one prominent Brexit campaigner said that “If it were up to me, I’d privatise the NHS.” – which of course had Emma Reynolds, a Labour MP, saying that vast numbers of Leave campaigners would like to privatise this “cherished national institution.”

Oh dear. There definitely is a case for reforming the NHS, as even those who work in it increasingly agree. Nobody can manage top-down nationalized industry of more than a million employees, nor make a state monopoly efficient. Perhaps instead the government should fund patients who need support, and let everyone shop around in an open healthcare market – or any of 101 other possible models that work well elsewhere. But the future of the NHS is a difficult and sensitive problem that needs rational thought and public debate. To talk about ‘privatising’ it is crass. Linking it to Brexit is just asking for trouble.

Of course, and just as outrageously, the Remain side have drafted the NHS into their arsenal too. They tell us that we have to stay in to save the NHS, which will lose research grants, have trouble recruiting nurses, and suffer all kinds of other problems. To a rational voter, this shroud-waving is equally dispiriting.

Let’s focus on the actual issues – economic, political, security, diplomatic – that June 23 is about. The NHS is not one of them.